KAHIBARO
Table of Contents
Sliding contact and friction
Kinetic friction is the frictional force that acts when two surfaces slide relative to each other. If a box is already moving across a floor, the friction opposing that motion is kinetic friction. It acts along the surface of contact and points opposite the direction of sliding.
This force appears because real surfaces are not perfectly smooth. At a microscopic level, tiny bumps and irregularities press against each other, and some energy is continuously transformed into thermal energy as the surfaces move.
Direction of kinetic friction
The direction of kinetic friction is always opposite the relative motion between the surfaces at the contact point. If a block slides to the right across a table, the kinetic friction on the block points to the left.
It is important to say relative motion. If one surface moves under another, friction depends on how the two surfaces slide with respect to each other, not just on what looks stationary in the room.
Magnitude of kinetic friction
For many introductory physics problems, the magnitude of kinetic friction is modeled by
$$
f_k = \mu_k N
$$
where $f_k$ is the kinetic friction force, $\mu_k$ is the coefficient of kinetic friction, and $N$ is the normal force.
The coefficient $\mu_k$ depends on the pair of materials in contact. It is a pure number, with no units.
For kinetic friction,
$$
f_k = \mu_k N
$$
This formula is one of the main rules for sliding friction in beginner mechanics.
The coefficient of kinetic friction
The coefficient of kinetic friction, written as $\mu_k$, tells us how strong the kinetic friction is for a given normal force. Larger $\mu_k$ means stronger friction.
Different surfaces have different values. A rubber surface on rough concrete usually has a larger coefficient than steel on ice. In simple physics models, $\mu_k$ is treated as constant, although in real life it can depend on conditions such as surface finish, temperature, and lubrication.
| Surface pair | Typical behavior of $\mu_k$ |
|---|---|
| Ice on ice | Very small |
| Wood on wood | Moderate |
| Rubber on rough road | Relatively large |
Relationship to the normal force
Kinetic friction is proportional to the normal force. If the surfaces are pressed together more strongly, the friction usually becomes larger. On a horizontal surface, the normal force is often equal to the weight of the object, but not always. On an incline or with extra applied forces, the normal force changes, and so does the kinetic friction.
This means you should first find $N$, then use $f_k = \mu_k N$.
Kinetic friction compared with static friction
Kinetic friction acts during sliding. Static friction acts when surfaces are not sliding relative to each other. In many cases, kinetic friction is smaller than the maximum possible static friction for the same surfaces.
That is why it is often harder to start pushing an object than to keep it moving once it has started.
Kinetic friction applies only when surfaces are sliding relative to each other.
Static friction applies when there is no sliding at the contact surface.
Effect on motion
Because kinetic friction opposes motion, it often causes moving objects to slow down if no other force keeps them moving. If kinetic friction is the only horizontal force on a sliding object, then the net force is opposite the motion, so the acceleration is also opposite the motion.
On a horizontal surface, if friction is the only horizontal force, then
$$
F_{\text{net}} = -f_k = -\mu_k N
$$
and if $N = mg$, then
$$
F_{\text{net}} = -\mu_k mg
$$
Using Newton's second law,
$$
a = \frac{F_{\text{net}}}{m} = -\mu_k g
$$
So the object has a constant acceleration opposite its direction of motion.
For a sliding object on a horizontal surface, if kinetic friction is the only horizontal force,
$$
a = -\mu_k g
$$
The negative sign shows that the acceleration is opposite the motion.
A simple example
Suppose a $5\,\text{kg}$ block slides on a horizontal floor with coefficient of kinetic friction $\mu_k = 0.20$. Take $g = 9.8\,\text{m/s}^2$.
First find the normal force:
$$
N = mg = 5 \times 9.8 = 49\,\text{N}
$$
Then the kinetic friction is
$$
f_k = \mu_k N = 0.20 \times 49 = 9.8\,\text{N}
$$
So the friction force has magnitude $9.8\,\text{N}$ and acts opposite the motion.
The acceleration is
$$
a = \frac{-9.8}{5} = -1.96\,\text{m/s}^2
$$
The block slows down at a constant rate.
Kinetic friction on an incline
On an inclined plane, the friction force still opposes sliding along the surface. The normal force is no longer equal to the full weight. If the incline angle is $\theta$, then
$$
N = mg\cos\theta
$$
so the kinetic friction becomes
$$
f_k = \mu_k mg\cos\theta
$$
If the block slides down the incline, friction points up the incline. If the block is pulled up the incline and slides upward, friction points down the incline.
Limits of the simple model
The equation $f_k = \mu_k N$ is a useful model for many basic problems, but it is still a model. Real friction can be more complicated. It may vary with speed, surface condition, temperature, or lubrication. Still, for introductory mechanics, this equation works well in many situations.
Key idea
Kinetic friction is the force that resists sliding motion between surfaces. In simple mechanics problems, its magnitude is found from the normal force and the coefficient of kinetic friction, and its direction is always opposite the sliding motion.
Main facts about kinetic friction:
$$
f_k = \mu_k N
$$
It acts opposite the relative sliding motion.
It depends on the normal force and the surface pair.